Help maths to work out how much electric peak and off peak used.

[ericmark]

I have on the app kWh or £ and I know peak 31.31p per kWh and off peak 8.95p per kWh, I want to know how many kWh at peak and how many at off peak, I have used excel and had it change ratio so found 9.19 kWh total was approx 5.93 kWh off peak and 3.26 kWh peak, but did it by changing the ratio 0.01 kWh at a time and read it where result was £1.55. But must be an easy way to write a formula to give a direct result.

Just having a senior moment can't work out how.

What I want to see is if I get a second battery how many days will it mean only use off peak.

 

[big-all]

it can be no more than number off units used at 31.31 =
and number off units used at 8.95=
the only other add on is standing charge and 5% vat but not a difficult point to work out ----with a clear head in the morning well after beer o clock

 

[JohnW2]

I have on the app kWh or £ and I know peak 31.31p per kWh and off peak 8.95p per kWh, I want to know how many kWh at peak and how many at off peak, I have used excel and had it change ratio so found 9.19 kWh total was approx 5.93 kWh off peak and 3.26 kWh peak, but did it by changing the ratio 0.01 kWh at a time and read it where result was £1.55. But must be an easy way to write a formula to give a direct result. .. Just having a senior moment can't work out how.

There's nothing wrong with the 'numerical' ('iterative') method you've used, which gives the correct answers but, as you surmise, it's not actually necessary because a ('closed form') formula is easy enough to derive. It's just a matter of solving a pair of simultaneous equations ...

Let:
X be kWh at peak rate,
Y be kWh at off-peak rate,
T be total kWh
P be total price (£) (but see below)

Then:
0.3131X + 0.0895 Y = P .... eqn(1)
and:
X + Y = T hence Y = T-X ... eqn(2)

Substituting eqn(2) into eqn(1) gives:
0.3131X + 0.0895 (T - X) = P
hence: 0.3131X + 0.0895T - 0.0895X = P
hence: 0.2236X + 0.0895T = P

Hence: X = (P - 0.0895T) / 0.2236

With your figures of P = 1.55 and T = 9.19, that gives X = 3.25, whence Y = 9.19 - 3.25 = 5.94 - the same answers you got.

However, as big-all has pointed out, if your app is anything like the IHDs which come with 'smart' meters, it might well be adding on the daily standing charge onto the usage charges to get what it displays as "£", in which case you would need to subtract that before applying the formula

What I want to see is if I get a second battery how many days will it mean only use off peak.

Fair enough. What would a second battery (and any y other frequired bits) cost?

 

[ericmark]

The second battery will cost around £1000 fitted, the app on the phone has a switch to add standing charge or show without standing charge. The formula you have given is spot on, now entered as an excel sheet, second battery is 3.2 kWh so on day given as an example it will means most power used will be off peak. But second advantage, think the inverter can handle 5 kW but battery max charging rate is 2 kW so even with half charged battery I end up exporting and producing over 2 kW, solar is rarely over 4 kW so second battery means will not export as much, as well as using more off peak and less peak power.

We will still need the grid for a shower etc during peak times, but in the main we will use no peak power.
Before solar the monthly payment was £173.90
After fitting went to £119.70
After off peak started £81.35
And we are £984.36 in credit so needs to be reduced further.
Actual usage can only really see since smart meter fitted, Jan smart meter fitted, hence low, the marked drop April to May was due to using off peak, set to kWh rather than £ the sharp drop is not there, a rough calculation solar saving around £40 per month, and battery around £20 per month existing battery 3.2 kWh, but also first battery means we have an UPS so heating still works when we have a power cut, also freezers, so there was an added benefit, piece of mind, the wood store in case we need to light a fire is reduced.

However we have also altered life style a little, the three machines dish washer, washing machine, tumble drier either over night or before 4 pm depending of how much solar, and during day not run together, even coffee would make two cups at same time, now one after the other. The latter can return to two together once we have second battery if we wanted.

All in all yes solar has been good, but value for money the battery has done better than solar, don't think solar would have really worked without the battery, as you can't rely on getting enough solar to run a tumble drier for 2.5 hours, you would have to switch it off each time a cloud came over.

Program has worked well

clearly the battery will help more in winter than summer using 602 watt/hours as on the 9th battery will do nothing really, but it does seem on average it will pay for its self. Thanks.

 

[JohnW2]

The second battery will cost around £1000 fitted,

Fair enough. Have you estimated how long it would be likely to take to get that £1,000 back from the 'savings' in bills (aka for how long you would be 'worse off' by having bought the additional battery)?

the app on the phone has a switch to add standing charge or show without standing charge.

That's good. Most IHDs I've seen don't seem to offer that choice, which can be a bit confusing!

The formula you have given is spot on, now entered as an excel sheet,

Glad it worked for you - as I said, it's pretty simple maths.

I obviously produced a formula using the current peak and off-peak prices, but it obviously could easily be adapted for any other figures. As well as changing the off-peak cost per kWh (£0.089 5 in my formula), the only thing you would have to re-calculate would be the final figure in my formula (0.2236), which is simply the difference between the peak and off-peak prices per kWh. If you wanted a 'general formula' into which you could plug any costs/kWh, then ...

If you add terms of C1 (cost in £ per peak kWh) and C2 (cost in £ per off-peak kWh, then my formula would become:

X = (P - {C2 * T} ) / (C1 - C2)

 

[ericmark]

I had modified as you show, I should have been able to do it, but had a mental block.

Also took ages to find out how to get rows to letters, so could use $ in front of tariffs so always uses same reference.

It worked a treat, thanks,

 

[JohnW2]

I had modified as you show, I should have been able to do it, but had a mental block.

We all have those - as well as moments of 'mental craziness'

Also took ages to find out how to get rows to letters, so could use $ in front of tariffs so always uses same reference.

That's a general truth about Excel - you have to priced the reference to a row or column with a dollar sign if you want it to be 'absolute' (always the same -... e.g. $A$2 if you want it to always to refer to cell A2 - or $A2 if you want it to always refer to column A, but want the row to be able to vary.

It worked a treat, thanks,

You're welcome. I'm glad it workes for you.

Kind Regards, John